A First Course In Probability, Global Edition
10th Edition
ISBN: 9781292269207
Author: Ross, Sheldon
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 7, Problem 7.32P
To determine
Tofind:the variance of the number of empty urns.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 7.5.
You repeatedly and independently spin a uniform spinner with three
colored regions: yellow, blue, and red. After 1800 spins, you tally the number of times your
spinner landed on red.
Independently from the spinner, you randomly extract balls from an urn containing 7 teal
and 21 beige balls with replacement. After 1000 extractions, you tally the number of times a
teal ball was extracted.
What is the variance of the difference between the number of times your spinner landed on
red and the number of times a teal ball was extracted?
5. One sample has SS = 70 and a second sample has
variances, and calculate the pooled variance.
a. If n = 8 for both samples, find each of the sample
One sample has SS = 70 and a second sample has
%3D
SS = 42.
If n = 8 for both samples, find each of the sample
variances, and calculate the pooled variance.
Because the samples are the same size, you should
find that the pooled variance is exactly halfway
%3D
%3D
between the two sample variances.
b. Now assume that n = 8 for the first sample and n
4 for the second. Again, calculate the two sam-
ple variances and the pooled variance. You should
find that the pooled variance is closer to the vari-
ance for the larger sample.
!וייייויוי"ויויויוי
CA 92251-0937
37
17
IRRIGATION DISTRICT
4)
2) If all of the values in a set of data were doubled, what would happen to the variance?
Chapter 7 Solutions
A First Course In Probability, Global Edition
Ch. 7 - A player throws a fair die and simultaneously...Ch. 7 - The game of Clue involves 6 suspects, 6 weapons,...Ch. 7 - Gambles are independent, and each one results in...Ch. 7 - Prob. 7.4PCh. 7 - The county hospital is located at the center of a...Ch. 7 - A fair die is rolled 10 times. Calculate the...Ch. 7 - Suppose that A and B each randomly and...Ch. 7 - N people arrive separately to a professional...Ch. 7 - A total of n. balls, numbered 1 through n, are put...Ch. 7 - Consider 3 trials, each having the same...
Ch. 7 - Consider n independent flips of a coin having...Ch. 7 - A group of n men and n women is lined up at...Ch. 7 - A set of 1000 cards numbered 1 through 1000 is...Ch. 7 - An urn has m black balls. At each stage, a black...Ch. 7 - In Example 2h, say that i and j, ij form a matched...Ch. 7 - Let Z be a standard normal random variable, and,...Ch. 7 - A deck of n cards numbered 1 through n is...Ch. 7 - Cards from an ordinary deck of 52 playing cards...Ch. 7 - Prob. 7.19PCh. 7 - Prob. 7.20PCh. 7 - For a group of 100 people, compute a. the expected...Ch. 7 - How many times would you expect to roll a fair die...Ch. 7 - Urn I contains 5 white and 6 black balls, while...Ch. 7 - A bottle initially contains m large pills and n...Ch. 7 - Let X1,X2... be a sequence of independent and...Ch. 7 - If X1,X2,....Xn are independent and identically...Ch. 7 - If 101 items are distributed among 10 boxes, then...Ch. 7 - Prob. 7.28PCh. 7 - There are 4 different types of coupons, the first...Ch. 7 - If X and Y are independent and identically...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - If E[X]=1 and Var(X)=5, find a. E[(2+X)2]: b....Ch. 7 - If 10 married couples are randomly seated at a...Ch. 7 - Cards from an ordinary deck are turned face up one...Ch. 7 - Let X be the number of ls and F the number of 2s...Ch. 7 - A die is rolled twice. Let X equal the sum of the...Ch. 7 - Suppose X and Y have the following joint...Ch. 7 - Suppose that 2 balls are randomly removed from an...Ch. 7 - Prob. 7.40PCh. 7 - Let X1,... be independent with common mean and...Ch. 7 - Prob. 7.42PCh. 7 - A pond contains 100 fish, of which 30 are carp. If...Ch. 7 - A group of 20 people consisting of 10 men and 10...Ch. 7 - Let X1,X2,...,Xn be independent random variables...Ch. 7 - Between two distinct methods for manufacturing...Ch. 7 - Prob. 7.47PCh. 7 - Consider the following dice game. as played at a...Ch. 7 - Prob. 7.49PCh. 7 - A fair die is successively rolled. Let X and Y...Ch. 7 - There are two misshapen coins in a box; their...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - A population is made up of r disjoint subgroups....Ch. 7 - A prisoner is trapped in a cell containing 3...Ch. 7 - Consider the following dice game: A pair of dice...Ch. 7 - Ten hunters are waiting for ducks to fly by. When...Ch. 7 - The number of people who enter an elevator on the...Ch. 7 - Suppose that the expected number of accidents per...Ch. 7 - A coin having probability p of coming up heads is...Ch. 7 - A coin that comes up heads with probability p is...Ch. 7 - There are n+1 participants in a game. Each person...Ch. 7 - Each of m+2 players pays 1 unit to a kitty in...Ch. 7 - The number of goals that J scores in soccer games...Ch. 7 - Prob. 7.65PCh. 7 - Prob. 7.66PCh. 7 - Prob. 7.67PCh. 7 - Prob. 7.68PCh. 7 - Type i light bulbs function for a random amount of...Ch. 7 - The number of winter storms in a good year is a...Ch. 7 - In Example 5c, compute the variance of the length...Ch. 7 - Prob. 7.72PCh. 7 - The number of accidents that a person has in a...Ch. 7 - Repeat Problem 7.73 when the proportion of the...Ch. 7 - Consider an urn containing a large number of...Ch. 7 - In problem ,suppose that the coin is tossed n...Ch. 7 - Suppose that in Problem 7.75, we continue to flip...Ch. 7 - In Example 6b, let S denote the signal sent and R...Ch. 7 - In Example 6c y)2].Ch. 7 - The moment generating function of X is given by...Ch. 7 - Let X be the value of the first die and Y the sum...Ch. 7 - The joint density of X and Y is given by...Ch. 7 - Prob. 7.83PCh. 7 - Successive weekly sales, in units of $1,000, have...Ch. 7 - Show that E[(Xa)2] is minimized at a=E[X].Ch. 7 - Suppose that X is a continuous random variable...Ch. 7 - Prob. 7.3TECh. 7 - Let X be a random variable having finite...Ch. 7 - Prob. 7.5TECh. 7 - Prob. 7.6TECh. 7 - Prob. 7.7TECh. 7 - We say that X is stochastically larger than Y,...Ch. 7 - Prob. 7.9TECh. 7 - A coin having probability p of landing on heads is...Ch. 7 - Let X1,X2,....Xn be independent and identically...Ch. 7 - Prob. 7.12TECh. 7 - Let X1,X2,... be a sequence of independent random...Ch. 7 - Prob. 7.14TECh. 7 - Prob. 7.15TECh. 7 - Prob. 7.16TECh. 7 - Prob. 7.17TECh. 7 - Prob. 7.18TECh. 7 - In Example 41 t, we showed that the covariance of...Ch. 7 - Show that X and Y are identically distributed and...Ch. 7 - Prob. 7.21TECh. 7 - Prob. 7.22TECh. 7 - Prob. 7.23TECh. 7 - Show that Z is a standard normal random variable...Ch. 7 - Prove the Cauchy-Schwarz inequality, namely,...Ch. 7 - Show that if X and Y are independent, then...Ch. 7 - Prove that E[g(X)YX]=g(X)E[YX].Ch. 7 - Prove that if E[YX=x]=E[Y] for all x, then X and Y...Ch. 7 - Prob. 7.29TECh. 7 - Let X1,...,Xn be independent and identically...Ch. 7 - Consider Example 4f, which is concerned with the...Ch. 7 - An urn initially contains b black and w white...Ch. 7 - For an event A, let IA equal 1 if A occurs and let...Ch. 7 - A coin that lands on heads with probability p is...Ch. 7 - For another approach to Theoretical Exercise 7.34,...Ch. 7 - The probability generating function of the...Ch. 7 - One ball at a time is randomly selected from an...Ch. 7 - Prob. 7.38TECh. 7 - Prob. 7.39TECh. 7 - The best quadratic predictor of Y with respect to...Ch. 7 - Use the conditional variance formula to determine...Ch. 7 - Let X be a normal random variable with parameters...Ch. 7 - It follows from Proposition 6.1 and the fact that...Ch. 7 - Show that for random variables X and Z,...Ch. 7 - Prob. 7.45TECh. 7 - Verify the formula for the moment generating...Ch. 7 - For a standard normal random variable Z, let...Ch. 7 - Prob. 7.48TECh. 7 - Prob. 7.49TECh. 7 - The positive random variable X is said to be a...Ch. 7 - Let X have moment generating function M(t), and...Ch. 7 - Use Table 7.2 to determine the distribution of...Ch. 7 - Show how to compute cov(X,Y) from the joint moment...Ch. 7 - Suppose that X1,...,Xn have a multivariate normal...Ch. 7 - If Z is a standard normal random variable, what is...Ch. 7 - Suppose that Y is a normal random variable with...Ch. 7 - Consider a list of m names, where the same name...Ch. 7 - Prob. 7.2STPECh. 7 - Prob. 7.3STPECh. 7 - Prob. 7.4STPECh. 7 - Prob. 7.5STPECh. 7 - Prob. 7.6STPECh. 7 - Prob. 7.7STPECh. 7 - Prob. 7.8STPECh. 7 - Prob. 7.9STPECh. 7 - Prob. 7.10STPECh. 7 - Prob. 7.11STPECh. 7 - Prob. 7.12STPECh. 7 - Prob. 7.13STPECh. 7 - Prob. 7.14STPECh. 7 - Prob. 7.15STPECh. 7 - Prob. 7.16STPECh. 7 - Prob. 7.17STPECh. 7 - Prob. 7.18STPECh. 7 - There are n items in a box labeled H and m in a...Ch. 7 - Let X be a nonnegative random variable having...Ch. 7 - Let a1,...,an, not all equal to 0, be such that...Ch. 7 - Prob. 7.22STPECh. 7 - Prob. 7.23STPECh. 7 - Prob. 7.24STPECh. 7 - Prob. 7.25STPECh. 7 - Prob. 7.26STPECh. 7 - Prob. 7.27STPECh. 7 - Prob. 7.28STPECh. 7 - Prob. 7.29STPECh. 7 - Prob. 7.30STPECh. 7 - Prob. 7.31STPECh. 7 - Prob. 7.32STPECh. 7 - Prob. 7.33STPE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- 2b. It is thought that 20% of Annual Tax returns to the Australian Tax Office (ATO) contain errors of one kind or another. An auditor in the ATO investigating the number of returns with errors in a particular industry takes a sample of 25 returns and classifies each return as being “in error” or “not in error”. i. If the variable X is used to represent the number of returns in the sample that are in error, and assuming this industry is no different to other industries in terms of the error rate, then state:• the values that X may take;• the distribution of this variable; and • the parameter/s of this distribution. ii. Determine the probability that 6 or less returns in this sample are in error. The auditor found that there were 13 tax returns with errors in this sample. iii. Determine the probability of finding 13 or more returns with errors if indeed the error rate was 20%. iv. Based upon your answer for part iii., what conclusion might the auditor make about this particular industry…arrow_forwardFrom the urn of Problem 1, ten balls are selected with replacement. Color Red Blue Green BrownNumber 4 3 2 1◼ 3.1. Estimate the probability that four or less red balls are selected.◼ 3.2. Estimate the probability that more than four blue balls are selected.arrow_forwardProblem: Random samples of size N=2 are drawn from a finite population consisting of the number 5,6,7,8 and 9. Compute for the mean, variance and standard deviation of the population, and the mean, variance and standard deviation of the sample meansarrow_forward
- In an analysis of variance problem if SST = 120 and SSTR = 90, then SSE isarrow_forwardAssume that the population consists of only these eleven data points for y and z. Construct one sample for y and one another sample for z by using 5 data points which gives the maximum variance. How can i do that. Thank youarrow_forwardA biased die is thrown thirty times and the number of sixes seen is eight. If the dic is thrown a further twelve times, the variance of the number of SIXES 1S =mmmmmmmmmmm .arrow_forward
- In testing the lethal concentration of a chemical found in polluted water, it is found that a certain concentration will kill 20% of the fish that are subjected to it for 24 hours. If 20 fish are placed in a tank containing this concentration of the chemical, a) find the number expected to survive out of 20 b) Find the variance of the number of survivors out of 20.arrow_forwardSuppose bob flips a fair coin 100 times.Let X be the number of heads he gets.What is Variance of X?arrow_forwardEvery day Roscoe G. Maples flips a fair coin four times and if it is heads all four times, he gives a dollar to charity. In a year with 365 days, what is Roscoe's expected annual donation to charity and what is the variance?arrow_forward
- 3. Sandpaper is rated by the coarseness of the grit on the paper. Sandpaper that is more coarse will remove material faster. Jobs that involve the final sanding of bare wood prior to painting or sanding in between coats of paint require sandpaper that is much finer. A manufacturer of sandpaper rated 220, which is used for the final preparation of bare wood, wants to make sure that the variance of the diameter of the particles in their 220 sandpaper does not exceed 2.0 micrometers. Fifty-one randomly selected particles are measured. The variance of the particle diameters is 2.13 micrometers. Assume that the distribution of particle diameter is approximately normal. a.Construct the 95% confidence intervals for the population variance and standard deviation b.Test at a 2.5% significance level whether the variance of the particle diameters of all particles in 220-rated sandpaper is greater than 2.0 micrometersarrow_forward1-arrow_forward9. A recent study claims that using music in a class enhances concentration and consequently helps students absorb more information. A researcher decided to test this claim on a smaller group of randomly selected students from three different classes. Each classroom was provided with a different environment for students to study. Classroom A had constant music being played in the background, classroom B had variable music being played and classroom C was a regular class with no music playing. After one month, the researcher conducted a test for all the three groups and ranked their scores. What statistical test would be most appropriate for testing the research hypothesis? Explain your answer.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY